Spherical Boundary Conditions Research Articles

Quantum mechanics/fluctuating charge calculations for absorption spectra of aqueous green fluorescent protein chromophore

AbstractWe applied the quantum mechanics/fluctuating charges (QM/FQ) method to simulate the absorption spectra of three protonated forms of p‐hydroxybenzylidene imidazolone (p‐HBDI) in water. Configurations of solute‐solvent were generated from molecular dynamics (MD) simulation within the context of a hybrid scheme in which solute and solvents were treated at QM and molecular mechanics, respectively. Nonperiodic spherical boundary condition was used. To examine the influence on simulated spectra coming from the geometrical relaxation of solute, the MD simulations were carried out for two cases: frozen and flexible molecular geometry of solute. As a result of our calculations, the simulations using the flexible solute's structure delivered vertical excitation energies closer to experimental data than those of a frozen solute, especially for the neutral case. For spectral broadening, changing from fixed geometry of solute to a flexible one led to a significant increase for both neutral and anionic forms of p‐HBDI, but no effect happened for the cationic one.

Configurational entropy of colloidal particles in a confined space.

We calculate the configurational entropy of colloidal particles in a confined geometry interacting as hard disks using Monte Carlo integration. In particular, we consider systems with three kinds of boundary conditions: hard, periodic, and spherical. For small to moderate packing fraction ϕ values, we find the entropies per particle for systems with the periodic and the spherical boundary conditions tend to reach the same value with the increase of the particle number N, while that for the system with the hard boundary conditions still has obvious differences compared to them within the studied N range. Surprisingly, despite the small system sizes, the estimated entropies per particle at infinite system size from extrapolations in the periodic and spherical systems are in reasonable agreement with that calculated using thermodynamic integration. Besides, as N increases we find the pair correlation function begins to exhibit similar features as that of a thermally equilibrated hard-disk fluid at the same packing fraction. Our findings may contribute to a better understanding of how the configurational entropy changes with the system size and the influence of boundary conditions, and provide insights relevant to engineering particles in confined spaces.

An efficient semi-analytical procedure to calculate acoustic radiation force and torque for axisymmetric irregular bodies

With the attributes of being biocompatible, label-free, and contact-free, sound has been widely used to manipulate micro-objects, such as cells, soft matters, and living things, by the acoustic radiation force and torque arising from wave scattering. The analytical theory exists for the acoustic radiation force and torque on separable geometries, including sphere and ellipsoid. However, it is still a challenge to handle irregular surfaces subject to non-orthogonal and inseparable boundary conditions. Here, we present a calculation method for an axisymmetric geometry with irregular cross-section excited by a time-harmonic plane wave with arbitrary incidence in the inviscid fluid. The method is based on conformal mapping from the irregular surface to a sphere in the new coordinate system. In this way, the separation of variables can be used to solve the corresponding Helmholtz wave equation subjecting to the spherical boundary conditions in the new coordinate system. The radiation force and the torque are asymptotically obtained using the far-field, closed-form solutions. The method is validated by comparisons with full 3D numerical solutions over a wide range of frequencies and incident angles. With a typical discrepancy of less than 5%, the proposed method is much more efficient than the full numerical simulations (via finite element method). Furthermore, it is found that the radiation force acting on different geometries follows the same tendency. The difference is that the presence of the radiation torque ensures that the symmetry axis of the irregular bodies is coincident with or orthogonal to the wave propagating direction.

Unifying Single-Channel Permeability From Rare-Event Sampling and Steady-State Flux.

Various all-atom molecular dynamics (MD) simulation methods have been developed to compute free energies and crossing rates of ions and small molecules through ion channels. However, a systemic comparison across different methods is scarce. Using a carbon nanotube as a model of small conductance ion channel, we computed the single-channel permeability for potassium ion using umbrella sampling, Markovian milestoning, and steady-state flux under applied voltage. We show that a slightly modified inhomogeneous solubility-diffusion equation yields a single-channel permeability consistent with the mean first passage time (MFPT) based method. For milestoning, applying cylindrical and spherical bulk boundary conditions yield consistent MFPT if factoring in the effective bulk concentration. The sensitivity of the MFPT to the output frequency of collective variables is highlighted using the convergence and symmetricity of the inward and outward MFPT profiles. The consistent transport kinetic results from all three methods demonstrated the robustness of MD-based methods in computing ion channel permeation. The advantages and disadvantages of each technique are discussed, focusing on the future applications of milestoning in more complex systems.

Variabilities in µQCT-based FEA of a tumoral bone mice model

A finite element analysis based on Micro-Quantitative Computed Tomography (µQCT) is a method with high potential to improve fracture risk prediction. However, the segmentation process and model generation are generally not automatized in their entirety. Even with a rigorous protocol, the operator might add uncertainties during the creation of the model. The aim of this study was to evaluate a µQCT-based model of mice tumoral and sham tibias in terms of the variabilities induced by the operator and sensitivity to operator-dependent variables (such as model orientation or length). Two different operators generated finite element (FE) models from µCT images of 8 female Balb/c nude mice tibias aged 10 weeks old with bone tumors induced in the right tibia and with sham injection in the left. From these models, predicted failure load was determined for two different boundary conditions: fixed support and spherical joints. The difference between the predicted and experimental failure load of both operators was large (-122% to 93%). The difference in the predicted failure load between operators was less for the spherical joints boundary conditions (9.8%) than for the fixed support (58.3%), p < 0.001, whereas varying the orientation of bone tibia caused more variability for the fixed support boundary condition (44.7%) than for the spherical joints (9.1%), p < 0.002. Varying tibia length had no significant effect, regardless of boundary conditions (<4%). When using the same mesh and same orientation, the difference between operators is non-significant (<6%) for each model. This study showed that the operator influences the failure load assessed by a µQCT-based finite element model of the tumoral and sham mice tibias. The results suggest that automation is needed for better reproducibility.

Method for Calculating the Optical Properties of Composites Based on a Transparent Matrix with Residual Porosity and Metal Nanoparticles

A method is proposed for calculating the optical characteristics of composites based on a transparent matrix with residual porosity and metal nanoparticles by solving the transport equation for monochromatic radiation employing a spherical harmonic method and Fresnel boundary conditions. The method is tested by modeling the transport of monochromatic radiation at four wavelengths of practical importance in cyclotrimethylenetrinitramine–aluminum nanoparticle composites with a Rayleigh distribution of pores with respect to radius. It is shown that in the case of small-radius pores the reflectivity increases as the mass fraction of nanoparticles is increased. In the case of pores with large radii, a kink corresponding to complete filling of the pores appears on the dependence of the transmission on the nanoparticle mass fraction. The application of these results to inverse problems in the spectroscopy of lightscattering system is discussed.

A simple, parameter-free method for computing solvation free energies of ions

Solvation free energies of ions are difficult to determine from molecular dynamics simulations due to the long-range Coulomb interactions. Various approximations and corrections are introduced to enable their calculation in small systems, which, however, raises issues of robustness. We show that solvation free energies of ions can be calculated using the spherical boundary conditions without introducing any corrections at the boundary via a buffer zone. The results are shown to converge for a droplet size of 21 Å and are independent of the parameters used for confining water or restraining the ion. The proposed method thus resolves the robustness issues in solvation free energy calculations of ions and can be used with confidence to determine force field parameters from such calculations. We apply the method to calculate the solvation free energies of the side chain analogs of charged amino acids. Tests using periodic boundary conditions show that similar results are also obtained in that case.

Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids

We present in this paper a spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) nodal values on a spherical surface. Built upon suitable analytic formulas for dealing with the involved highly oscillatory integrands, the method is robust for high mode expansions. We apply the numerical method to the simulation of three-dimensional acoustic and electromagnetic multiple scattering problems. Various numerical evidences show that the high accuracy can be achieved within reasonable computational time. This also paves the way for spectral-element discretization of 3D scattering problems reduced by spherical transparent boundary conditions based on the Dirichlet-to-Neumann map.

Simulating the absorption spectra of helium clusters (N = 70, 150, 231, 300) using a charge transfer correction to superposition of fragment single excitations.

Simulations of the n = 2 absorption spectra of HeN (N = 70, 150, 231, 300) clusters are reported, with nuclear configurations sampled by path integral molecular dynamics. The electronic structure is treated by a new approach, ALMO-CIS+CT, which is a formulation of configuration interaction singles (CIS) based on absolutely localized molecular orbitals (ALMOs). The method generalizes the previously reported ALMO-CIS model [K. D. Closser et al. J. Chem. Theory Comput. 11, 5791 (2015)] to include spatially localized charge transfer (CT) effects. It is designed to recover large numbers of excited states in atomic and molecular clusters, such as the entire n = 2 Rydberg band in helium clusters. ALMO-CIS+CT is shown to recover most of the error caused by neglecting charge transfer in ALMO-CIS and has comparable accuracy to standard CIS for helium clusters. For the n = 2 band, CT stabilizes states towards the blue edge by up to 0.5 eV. ALMO-CIS+CT retains the formal cubic scaling of ALMO-CIS with respect to system size. With improvements to the implementation over that originally reported for ALMO-CIS, ALMO-CIS+CT is able to treat helium clusters with hundreds of atoms using modest computing resources. A detailed simulation of the absorption spectra associated with the 2s and 2p bands of helium clusters up to 300 atoms is reported, using path integral molecular dynamics with a spherical boundary condition to generate atomic configurations at 3 K. The main features of experimentally reported fluorescence excitation spectra for helium clusters are reproduced.

Tracer diffusion in a polymer gel: simulations of static and dynamic 3D networks using spherical boundary conditions

We have investigated an alternative to the standard periodic boundary conditions for simulating the diffusion of tracer particles in a polymer gel by performing Brownian dynamics simulations using spherical boundary conditions. The gel network is constructed by randomly distributing tetravalent cross-linking nodes and connecting nearest pairs. The final gel structure is characterised by the radial distribution functions, chain lengths and end-to-end distances, and the pore size distribution. We have looked at the diffusion of tracer particles with a wide range of sizes, diffusing in both static and dynamic networks of two different volume fractions. It is quantitatively shown that the dynamical effect of the network becomes more important in facilitating the diffusional transport for larger particle sizes, and that one obtains a finite diffusion also for particle sizes well above the maximum in the pore size distribution.

Free Energies of Redox Half-Reactions from First-Principles Calculations.

Quantitative prediction of the energetics of redox half-reactions is still a challenge for modern computational chemistry. Here, we propose a simple scheme for reliable calculations of vertical ionization and attachment energies, as well as of redox potentials of solvated molecules. The approach exploits linear response approximation in the context of explicit solvent simulations with spherical boundary conditions. It is shown that both vertical ionization energies and vertical electron affinities, and, consequently redox potentials, exhibit linear dependence on the inverse radius of the solvation sphere. The explanation of the linear dependence is provided, and an extrapolation scheme is suggested. The proposed approach accounts for the specific short-range interactions within hybrid DFT and effective fragment potential approach as well as for the asymptotic system-size effects. The computed vertical ionization energies and redox potentials are in excellent agreement with the experimental values.

Three-dimensional spherical spatial boundary conditions differentially regulate osteogenic differentiation of mesenchymal stromal cells.

The spatial boundary condition (SBC) arising from the surrounding microenvironment imposes specific geometry and spatial constraints that affect organogenesis and tissue homeostasis. Mesenchymal stromal cells (MSCs) sensitively respond to alterations of mechanical cues generated from the SBC. However, mechanical cues provided by a three-dimensional (3D) environment are deprived in a reductionist 2D culture system. This study investigates how SBC affects osteogenic differentiation of MSCs using 3D scaffolds with monodispersed pores and homogenous spherical geometries. MSCs cultured under SBCs with diameters of 100 and 150 μm possessed the greatest capability of osteogenic differentiation. This phenomenon was strongly correlated with MSC morphology, organization of actin cytoskeleton, and distribution of focal adhesion involving α2 and α5 integrins. Further silencing either α2 or α5 integrin significantly reduced the above mentioned mechanosensitivity, indicating that the α2 and α5 integrins as mechano-sensitive molecules mediate MSCs’ ability to provide enhanced osteogenic differentiation in response to different spherical SBCs. Taken together, the findings provide new insights regarding how MSCs respond to mechanical cues from the surrounding microenvironment in a spherical SBC, and such biophysical stimuli should be taken into consideration in tissue engineering and regenerative medicine in conjunction with biochemical cues.

Plastic deformations in thin rotational shells

The paper focuses on the method of calculation of evolution shells beyond the elastic limit. The conclusion of the basic system of differential equations is based on the linear shell theory with regard to the Hirchhoff-Lave hypothesis and on the physical equations for small elastic-plastic deformation theory using the method of elastic decisions. The boundary conditions are formulated for Cauchy problem: rigid attachment, hinged support, and free margin. The spherical shell boundary conditions in the pole are obtained from the conditions of symmetry and antisymmetry functions. The convergence of the elastic method and the method of the occurrence of superficial plastic deformations are studied. Also the stress-strain state in the spherical shell is determined and the convergence of the obtained solutions was studied. The results are presented on the symmetric load ring applied to the middle of the Meridian and on the load that can be considered as a concentrated force. The sufficient quantity of iterations is established to achieve the accuracy of 0.1%. The graphs are presented for radial displacement and for meridional bending moment as the functions that converge more rapidly and more slowly respectively.

Scattering cluster wave functions on the lattice using the adiabatic projection method

The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. Previous studies have used the adiabatic projection method to extract scattering phase shifts from finite periodic-box energy levels using L\"uschers method. In this paper we demonstrate that scattering observables can be computed directly from asymptotic cluster wave functions. For a variety of examples in one and three spatial dimensions, we extract elastic phase shifts from asymptotic cluster standing waves corresponding to spherical wall boundary conditions. We find that this approach of extracting scattering wave functions from the adiabatic Hamiltonian to be less sensitive to small stochastic and systematic errors as compared with using periodic-box energy levels.

Interference by amplitude division with extended sources by paraxial boundary conditions

We present a wave-optics paraxial approach to the interference by amplitude division produced by plane-parallel films (or plates) and non-plane-parallel films, or by equivalent optical devices such as a Michelson interferometer, when they are illuminated with extended (spatially incoherent) quasi-monochromatic sources. To the best of our knowledge, the most common approaches to the study of interference are based, for simplicity, on the combined use of geometrical optics concepts, such as the optical path length along a ray, together with some wave-optics concepts such as optical phases. However, interference phenomena have been the means by which the wave nature of light has been established and therefore geometrical and wave concepts are so far-off that their simultaneous use can give rise to misleading concepts. Therefore, the primary aim of this work is to provide an analytical homogeneous description of interference by amplitude division using only paraxial spherical waves and boundary conditions at smooth interfaces or discontinuities in such a way that the calculation of the total optical field, interference irradiance, fringe visibility, coherence degree, localization of the interference and so on, can be made in a unified way by taking a fully wave-optics approach. The paraxial regime is enough in most cases and, moreover, interference is generally collected by an optical instrument such as a lens or the eye itself, in which a paraxial approximation is required. This work is particularly aimed at university physics teachers and undergraduate and first year postgraduate students.

Deterministic Greedy Routing with Guaranteed Delivery in 3D Wireless Sensor Networks

With both computational complexity and storage space bounded by a small constant, greedy routing is recognized as an appealing approach to support scalable routing in wireless sensor networks. However, significant challenges have been encountered in extending greedy routing from 2D to 3D space. In this research, we develop decentralized solutions to achieve greedy routing in 3D sensor networks. Our proposed approach is based on a unit tetrahedron cell (UTC) mesh structure. We propose a distributed algorithm to realize volumetric harmonic mapping (VHM) of the UTC mesh under spherical boundary condition. It is a one-to-one map that yields virtual coordinates for each node in the network without or with one internal hole. Since a boundary has been mapped to a sphere, node-based greedy routing is always successful thereon. At the same time, we exploit the UTC mesh to develop a face-based greedy routing algorithm and prove its success at internal nodes. To deliver a data packet to its destination, face-based and node-based greedy routing algorithms are employed alternately at internal and boundary UTCs, respectively. For networks with multiple internal holes, a segmentation and tunnel-based routing strategy is proposed on top of VHM to support global end-to-end routing. As far as we know, this is the first work that realizes truly deterministic routing with constant-bounded storage and computation in general 3D wireless sensor networks.

SCALAR CASIMIR EFFECT BETWEEN TWO CONCENTRIC SPHERES

The Casimir effect giving rise to an attractive force between the closely spaced two concentric spheres that confine the massless scalar field is calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We developed a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions. The Casimir energy for a massless scalar field between the closely spaced two concentric spheres coincides with the Casimir energy of the parallel plates for a massless scalar field in the limit when the dimensionless parameter η, ([Formula: see text] where a(b) is inner (outer) radius of sphere), goes to zero. The efficiency of new approach is demonstrated by calculation of the Casimir energy for a massless scalar field between the closely spaced two concentric half spheres.

MD–SAXS method with nonspherical boundaries

Small-angle X-ray solution scattering (SAXS) experiments provide information about protein structures in solution, albeit at low resolution. The molecular dynamics (MD)–SAXS method is capable of linking SAXS data and high-resolution atomic structures of proteins including hydrating water molecules. The MD–SAXS method, which was previously limited to spherical boundary conditions, is here extended to nonspherical boundary conditions while retaining accuracy. The method presented here is computationally effective, particularly for elongated proteins, because a number of water molecules can be eliminated compared to the original formulation.

Spontaneous counter-current imbibition outwards from a hemi-spherical depression

Spontaneous counter-current imbibition occurs when brine spontaneously displaces oil from a very strongly water-wet rock. Past experiments have been performed on cylindrical rock cores, with or without a cylindrical hole drilled through them, that have some or all of their faces open to imbibition. Changes in the area open to imbibition and the boundary conditions of the core plug can make large differences to the rate of imbibition. For example, linear imbibition into a core with one-end-open is significantly slower than imbibition into an all-faces-open core, and radial inwards imbibition goes faster than radial outwards imbibition. For linear imbibition, the volume imbibed with time varies as the square root of time as compared with almost linear variation with time for radial outwards imbibition. The reason for this behaviour during radial outwards imbibition is that most of the flow resistance is in the vicinity of the cylindrical hole, whereas most of the volume is near the closed outer boundary of the core. One would expect similar behaviour (i.e. imbibition volume linear with time) from spherical outwards imbibition. Experimentally, the situation can be realised by imbibition from an open hemi-spherical cavity on one face of a hemi-spherical block which is sealed on all other faces. In the present paper, a theory for spontaneous spherical outwards imbibition is developed assuming piston-like advance of a front from such a hemi-spherical cavity. Results are calculated and compared for various boundary conditions and the spherical outwards prediction is then tested by experimental results obtained for chalk blocks. The predictions and the experiments confirm that, for the spherical outwards boundary condition, the production curves can be almost linear with time.

Fast and Accurate Computation of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

This paper is concerned with fast and accurate computation of exterior wave equations truncated via exact circular or spherical nonreflecting boundary conditions (NRBCs, known to be nonlocal in both time and space). We first derive analytic expressions for the underlying convolution kernels, which allow for a rapid and accurate evaluation of the convolution with $O(N_t)$ operations over $N_t$ successive time steps. To handle the nonlocality in space, we introduce the notion of boundary perturbation, which enables us to handle general bounded scatters by solving a sequence of wave equations in a regular domain. We propose an efficient spectral-Galerkin solver with Newmark's time integration for the truncated wave equation in the regular domain. We also provide ample numerical results to show high-order accuracy of NRBCs and efficiency of the proposed scheme.